Abstract

Seven schemes are studied theoretically for Doppler-free two-photon excitation of rare 41Ca isotope using single-mode continuous-wave lasers. The ionization efficiencies and optical selectivities for all the schemes are calculated for various powers of the excitation and ionization lasers and for various focusing conditions of the two lasers. To maximize the ionization efficiencies and the optical selectivities, wavelength-dependent Stark compensation is used. Certain laser wavelengths of the ionization step termed as magic wavelengths are identified for compensating the Stark shift induced by the excitation laser. The effects of the Stark-shift-induced asymmetry and its reversal by selecting the appropriate magic wavelength for the ionization step for various excitation and ionization laser intensities are investigated. The ionization efficiency and optical selectivity for the best scheme after Stark compensation are found to be 8.4×10-4 and 9×103, respectively.

© 2006 Optical Society of America

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  1. K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
    [CrossRef]
  2. P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
    [CrossRef]
  3. M. Eisenbud, Environmental Radioactivity (Academic, 1987).
  4. M. G. Payne, L. Deng, and N. Thonnard, "Applications of resonance ionization mass spectrometry," Rev. Sci. Instrum. 65, 2433-2459 (1994).
    [CrossRef]
  5. H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
    [CrossRef]
  6. B. Dai and P. Lambropoulos, "Selective ionization: effects of power broadening, laser bandwidth, and interaction time on selectivity," Phys. Rev. A 34, 3954-3961 (1986).
    [CrossRef] [PubMed]
  7. P. Zoller and P. Lambropoulos, "Laser temporal coherence effects in two-photon resonant three-photon ionization," J. Phys. B 13, 69-83 (1980).
    [CrossRef]
  8. T. B. Lucatarto, C. W. Clark, and L. J. Moore, "Possibilities for ultrasensitive mass spectrometry based on two-photon, sub-Doppler resonance ionization," Opt. Commun. 48, 406-410 (1984).
    [CrossRef]
  9. A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
    [CrossRef]
  10. B. A. Bushaw, W. Nortershauser, and K. Wendt, "Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry," Spectrochim. Acta Part B 54, 321-332 (1999).
    [CrossRef]
  11. B. A. Bushaw and W. Nortershauser, Resonance ionization spectroscopy of stable strontium isotopes and 90Sr via 5s21S0 --> 5s5p 1P1 --> 5s5d 1D2 --> 5s11f 1F3 --> Sr," Spectrochim. Acta Part B 55, 1679-1692 (2000).
    [CrossRef]
  12. B. A. Bushaw, W. Nortershauser, G. Ewald, A. Dax, and G. W. F. Drake, "Hyperfine splitting, isotope shift, and level energy of the 3S States of 6,7Li," Phys. Rev. Lett. 91, 043004 (2003).
  13. G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).
  14. H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).
  15. C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, "Wavelength-dependent ac Stark shift of the 1S0-3P1 transition at 657 nm in Ca," Phys. Rev. A 70, 023414 (6) (2004).
  16. M. Sankari, P. V. Kirankumar, and M. V. Suryanarayana, "Wavelength-dependent Stark compensation in isotope selective Doppler-free two-photon ionization," Opt. Commun. 259, 612-619 (2006).
    [CrossRef]
  17. R. L. Kurucz and B. Bell, Atomic Line Data Kurucz CD-ROM No. 23 (Smithsonian Astrophysical Observatory, 1995).
  18. R. L. Kurucz, 1988, Trans. IAU, XXB, M.McNally, ed., (Kluwer, 1966) 168-172.
  19. W. L. Wiese, M. W. Smith, and B. M. Glennon, Atomic Transition Probabilities, Elements Hydrogen through Neon, NSRDS-NBS (Government Printing Office, 1966), p. 153.
  20. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990).
  21. T. Rickes, J. P. Marangos, T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
    [CrossRef]
  22. T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, "Lineshapes in coherent two-photon excitation," Opt. Commun. 220, 353-359 (2003).
    [CrossRef]
  23. B. A. Bushaw, "Diode-laser-based resonance ionization mass spectrometric measurement of calcium isotopes," Ph.D. dissertation (Johannes-Gutenberg Universitat, 1997).
  24. C. J. Lorenzen, K. Niemax, and L. R. Pendrill, "Isotope shifts of energy levels in the naturally abundant isotopes of strontium and calcium," Phys. Rev. A 28, 2051-2058 (1983).
    [CrossRef]

2006

M. Sankari, P. V. Kirankumar, and M. V. Suryanarayana, "Wavelength-dependent Stark compensation in isotope selective Doppler-free two-photon ionization," Opt. Commun. 259, 612-619 (2006).
[CrossRef]

2003

T. Rickes, J. P. Marangos, T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
[CrossRef]

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, "Lineshapes in coherent two-photon excitation," Opt. Commun. 220, 353-359 (2003).
[CrossRef]

2002

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

2000

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

B. A. Bushaw and W. Nortershauser, Resonance ionization spectroscopy of stable strontium isotopes and 90Sr via 5s21S0 --> 5s5p 1P1 --> 5s5d 1D2 --> 5s11f 1F3 --> Sr," Spectrochim. Acta Part B 55, 1679-1692 (2000).
[CrossRef]

1999

B. A. Bushaw, W. Nortershauser, and K. Wendt, "Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry," Spectrochim. Acta Part B 54, 321-332 (1999).
[CrossRef]

1994

M. G. Payne, L. Deng, and N. Thonnard, "Applications of resonance ionization mass spectrometry," Rev. Sci. Instrum. 65, 2433-2459 (1994).
[CrossRef]

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
[CrossRef]

1991

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

1986

B. Dai and P. Lambropoulos, "Selective ionization: effects of power broadening, laser bandwidth, and interaction time on selectivity," Phys. Rev. A 34, 3954-3961 (1986).
[CrossRef] [PubMed]

1984

T. B. Lucatarto, C. W. Clark, and L. J. Moore, "Possibilities for ultrasensitive mass spectrometry based on two-photon, sub-Doppler resonance ionization," Opt. Commun. 48, 406-410 (1984).
[CrossRef]

1983

C. J. Lorenzen, K. Niemax, and L. R. Pendrill, "Isotope shifts of energy levels in the naturally abundant isotopes of strontium and calcium," Phys. Rev. A 28, 2051-2058 (1983).
[CrossRef]

1980

P. Zoller and P. Lambropoulos, "Laser temporal coherence effects in two-photon resonant three-photon ionization," J. Phys. B 13, 69-83 (1980).
[CrossRef]

Aspect, A.

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

Bauche, J.

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

Becher, C.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Bell, B.

R. L. Kurucz and B. Bell, Atomic Line Data Kurucz CD-ROM No. 23 (Smithsonian Astrophysical Observatory, 1995).

Bergmann, K.

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, "Lineshapes in coherent two-photon excitation," Opt. Commun. 220, 353-359 (2003).
[CrossRef]

Blatt, R.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Blaum, K.

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

Bushaw, B. A.

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

B. A. Bushaw and W. Nortershauser, Resonance ionization spectroscopy of stable strontium isotopes and 90Sr via 5s21S0 --> 5s5p 1P1 --> 5s5d 1D2 --> 5s11f 1F3 --> Sr," Spectrochim. Acta Part B 55, 1679-1692 (2000).
[CrossRef]

B. A. Bushaw, W. Nortershauser, and K. Wendt, "Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry," Spectrochim. Acta Part B 54, 321-332 (1999).
[CrossRef]

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
[CrossRef]

B. A. Bushaw, "Diode-laser-based resonance ionization mass spectrometric measurement of calcium isotopes," Ph.D. dissertation (Johannes-Gutenberg Universitat, 1997).

B. A. Bushaw, W. Nortershauser, G. Ewald, A. Dax, and G. W. F. Drake, "Hyperfine splitting, isotope shift, and level energy of the 3S States of 6,7Li," Phys. Rev. Lett. 91, 043004 (2003).

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Clark, C. W.

T. B. Lucatarto, C. W. Clark, and L. J. Moore, "Possibilities for ultrasensitive mass spectrometry based on two-photon, sub-Doppler resonance ionization," Opt. Commun. 48, 406-410 (1984).
[CrossRef]

Dai, B.

B. Dai and P. Lambropoulos, "Selective ionization: effects of power broadening, laser bandwidth, and interaction time on selectivity," Phys. Rev. A 34, 3954-3961 (1986).
[CrossRef] [PubMed]

Dax, A.

B. A. Bushaw, W. Nortershauser, G. Ewald, A. Dax, and G. W. F. Drake, "Hyperfine splitting, isotope shift, and level energy of the 3S States of 6,7Li," Phys. Rev. Lett. 91, 043004 (2003).

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Degenhardt, C.

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, "Wavelength-dependent ac Stark shift of the 1S0-3P1 transition at 657 nm in Ca," Phys. Rev. A 70, 023414 (6) (2004).

Deng, L.

M. G. Payne, L. Deng, and N. Thonnard, "Applications of resonance ionization mass spectrometry," Rev. Sci. Instrum. 65, 2433-2459 (1994).
[CrossRef]

Diel, S.

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

Drake, G. W. F.

B. A. Bushaw, W. Nortershauser, G. Ewald, A. Dax, and G. W. F. Drake, "Hyperfine splitting, isotope shift, and level energy of the 3S States of 6,7Li," Phys. Rev. Lett. 91, 043004 (2003).

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Eisenbud, M.

M. Eisenbud, Environmental Radioactivity (Academic, 1987).

Eschner, J.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Ewald, G.

B. A. Bushaw, W. Nortershauser, G. Ewald, A. Dax, and G. W. F. Drake, "Hyperfine splitting, isotope shift, and level energy of the 3S States of 6,7Li," Phys. Rev. Lett. 91, 043004 (2003).

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Geppert, C.

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

Geppert, Ch.

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

Glennon, B. M.

W. L. Wiese, M. W. Smith, and B. M. Glennon, Atomic Transition Probabilities, Elements Hydrogen through Neon, NSRDS-NBS (Government Printing Office, 1966), p. 153.

Godefroid, M.

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

Gotte, S.

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Grangier, P.

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

Gulde, S.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Haffner, H.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Halfmann, T.

T. Rickes, J. P. Marangos, T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
[CrossRef]

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, "Lineshapes in coherent two-photon excitation," Opt. Commun. 220, 353-359 (2003).
[CrossRef]

Hansen, J. E.

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

Kirankumar, P. V.

M. Sankari, P. V. Kirankumar, and M. V. Suryanarayana, "Wavelength-dependent Stark compensation in isotope selective Doppler-free two-photon ionization," Opt. Commun. 259, 612-619 (2006).
[CrossRef]

Kirchner, R.

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Kluge, H.-J.

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
[CrossRef]

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Kuhl, Th.

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Kurucz, R. L.

R. L. Kurucz and B. Bell, Atomic Line Data Kurucz CD-ROM No. 23 (Smithsonian Astrophysical Observatory, 1995).

R. L. Kurucz, 1988, Trans. IAU, XXB, M.McNally, ed., (Kluwer, 1966) 168-172.

Lambropoulos, P.

B. Dai and P. Lambropoulos, "Selective ionization: effects of power broadening, laser bandwidth, and interaction time on selectivity," Phys. Rev. A 34, 3954-3961 (1986).
[CrossRef] [PubMed]

P. Zoller and P. Lambropoulos, "Laser temporal coherence effects in two-photon resonant three-photon ionization," J. Phys. B 13, 69-83 (1980).
[CrossRef]

Lancaster, G.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Lisdat, C.

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, "Wavelength-dependent ac Stark shift of the 1S0-3P1 transition at 657 nm in Ca," Phys. Rev. A 70, 023414 (6) (2004).

Lorenzen, C. J.

C. J. Lorenzen, K. Niemax, and L. R. Pendrill, "Isotope shifts of energy levels in the naturally abundant isotopes of strontium and calcium," Phys. Rev. A 28, 2051-2058 (1983).
[CrossRef]

Lucatarto, T. B.

T. B. Lucatarto, C. W. Clark, and L. J. Moore, "Possibilities for ultrasensitive mass spectrometry based on two-photon, sub-Doppler resonance ionization," Opt. Commun. 48, 406-410 (1984).
[CrossRef]

Marangos, J. P.

T. Rickes, J. P. Marangos, T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
[CrossRef]

Miyabe, M.

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

Moore, L. J.

T. B. Lucatarto, C. W. Clark, and L. J. Moore, "Possibilities for ultrasensitive mass spectrometry based on two-photon, sub-Doppler resonance ionization," Opt. Commun. 48, 406-410 (1984).
[CrossRef]

Muller, P.

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

Nahler, A.

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

Niemax, K.

C. J. Lorenzen, K. Niemax, and L. R. Pendrill, "Isotope shifts of energy levels in the naturally abundant isotopes of strontium and calcium," Phys. Rev. A 28, 2051-2058 (1983).
[CrossRef]

Nortershauser, W.

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

B. A. Bushaw and W. Nortershauser, Resonance ionization spectroscopy of stable strontium isotopes and 90Sr via 5s21S0 --> 5s5p 1P1 --> 5s5d 1D2 --> 5s11f 1F3 --> Sr," Spectrochim. Acta Part B 55, 1679-1692 (2000).
[CrossRef]

B. A. Bushaw, W. Nortershauser, and K. Wendt, "Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry," Spectrochim. Acta Part B 54, 321-332 (1999).
[CrossRef]

B. A. Bushaw, W. Nortershauser, G. Ewald, A. Dax, and G. W. F. Drake, "Hyperfine splitting, isotope shift, and level energy of the 3S States of 6,7Li," Phys. Rev. Lett. 91, 043004 (2003).

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Passler, G.

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
[CrossRef]

Payne, M. G.

M. G. Payne, L. Deng, and N. Thonnard, "Applications of resonance ionization mass spectrometry," Rev. Sci. Instrum. 65, 2433-2459 (1994).
[CrossRef]

Pendrill, L. R.

C. J. Lorenzen, K. Niemax, and L. R. Pendrill, "Isotope shifts of energy levels in the naturally abundant isotopes of strontium and calcium," Phys. Rev. A 28, 2051-2058 (1983).
[CrossRef]

Rickes, T.

T. Rickes, J. P. Marangos, T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
[CrossRef]

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, "Lineshapes in coherent two-photon excitation," Opt. Commun. 220, 353-359 (2003).
[CrossRef]

Riebe, M.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Riehle, F.

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, "Wavelength-dependent ac Stark shift of the 1S0-3P1 transition at 657 nm in Ca," Phys. Rev. A 70, 023414 (6) (2004).

Sanchez, R.

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Sankari, M.

M. Sankari, P. V. Kirankumar, and M. V. Suryanarayana, "Wavelength-dependent Stark compensation in isotope selective Doppler-free two-photon ionization," Opt. Commun. 259, 612-619 (2006).
[CrossRef]

Schmidt-Kaler, F.

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990).

Smith, M. W.

W. L. Wiese, M. W. Smith, and B. M. Glennon, Atomic Transition Probabilities, Elements Hydrogen through Neon, NSRDS-NBS (Government Printing Office, 1966), p. 153.

Sterr, U.

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, "Wavelength-dependent ac Stark shift of the 1S0-3P1 transition at 657 nm in Ca," Phys. Rev. A 70, 023414 (6) (2004).

Stoehr, H.

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, "Wavelength-dependent ac Stark shift of the 1S0-3P1 transition at 657 nm in Ca," Phys. Rev. A 70, 023414 (6) (2004).

Suryanarayana, M. V.

M. Sankari, P. V. Kirankumar, and M. V. Suryanarayana, "Wavelength-dependent Stark compensation in isotope selective Doppler-free two-photon ionization," Opt. Commun. 259, 612-619 (2006).
[CrossRef]

Thonnard, N.

M. G. Payne, L. Deng, and N. Thonnard, "Applications of resonance ionization mass spectrometry," Rev. Sci. Instrum. 65, 2433-2459 (1994).
[CrossRef]

Trautmann, N.

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
[CrossRef]

Vaeck, N.

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

Vitanov, N. V.

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, "Lineshapes in coherent two-photon excitation," Opt. Commun. 220, 353-359 (2003).
[CrossRef]

Wendt, K.

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

B. A. Bushaw, W. Nortershauser, and K. Wendt, "Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry," Spectrochim. Acta Part B 54, 321-332 (1999).
[CrossRef]

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
[CrossRef]

Wendt, K. D. A.

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

Wiese, W. L.

W. L. Wiese, M. W. Smith, and B. M. Glennon, Atomic Transition Probabilities, Elements Hydrogen through Neon, NSRDS-NBS (Government Printing Office, 1966), p. 153.

Wojtaszek, A.

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Yan, Z.-C.

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Zimmermann, C.

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

Zoller, P.

P. Zoller and P. Lambropoulos, "Laser temporal coherence effects in two-photon resonant three-photon ionization," J. Phys. B 13, 69-83 (1980).
[CrossRef]

Fresenius J. Anal. Chem.

H.-J. Kluge, B. A. Bushaw, G. Passler, K. Wendt, and N. Trautmann, "Resonance ionization spectroscopy for trace analysis and fundamental research," Fresenius J. Anal. Chem. 350, 323-329 (1994).
[CrossRef]

J. Nucl. Sci. Technol.

K. D. A. Wendt, C. Geppert, M. Miyabe, P. Muller, W. Nortershauser, and N. Trautmann, "Ultra trace isotope determination in environmental, biomedical, and fundamental research by high resolution laser-mass spectrometry," J. Nucl. Sci. Technol. 39, 303-307 (2002).
[CrossRef]

J. Phys. B

A. Aspect, J. Bauche, M. Godefroid, P. Grangier, J. E. Hansen, and N. Vaeck, "Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I," J. Phys. B 24, 4077-4099 (1991).
[CrossRef]

P. Zoller and P. Lambropoulos, "Laser temporal coherence effects in two-photon resonant three-photon ionization," J. Phys. B 13, 69-83 (1980).
[CrossRef]

Opt. Commun.

T. B. Lucatarto, C. W. Clark, and L. J. Moore, "Possibilities for ultrasensitive mass spectrometry based on two-photon, sub-Doppler resonance ionization," Opt. Commun. 48, 406-410 (1984).
[CrossRef]

T. Rickes, J. P. Marangos, T. Halfmann, "Enhancement of third-harmonic generation by Stark-chirped rapid adiabatic passage," Opt. Commun. 227, 133-142 (2003).
[CrossRef]

T. Halfmann, T. Rickes, N. V. Vitanov, and K. Bergmann, "Lineshapes in coherent two-photon excitation," Opt. Commun. 220, 353-359 (2003).
[CrossRef]

M. Sankari, P. V. Kirankumar, and M. V. Suryanarayana, "Wavelength-dependent Stark compensation in isotope selective Doppler-free two-photon ionization," Opt. Commun. 259, 612-619 (2006).
[CrossRef]

Phys. Rev. A

B. Dai and P. Lambropoulos, "Selective ionization: effects of power broadening, laser bandwidth, and interaction time on selectivity," Phys. Rev. A 34, 3954-3961 (1986).
[CrossRef] [PubMed]

C. J. Lorenzen, K. Niemax, and L. R. Pendrill, "Isotope shifts of energy levels in the naturally abundant isotopes of strontium and calcium," Phys. Rev. A 28, 2051-2058 (1983).
[CrossRef]

Radiochim. Acta

P. Muller, K. Blaum, B. A. Bushaw, S. Diel, Ch. Geppert, A. Nahler, W. Nortershauser, N. Trautmann, and K. Wendt, "Trace detection of 41Ca in nuclear reactor concrete by diode-laser-based resonance ionization mass spectrometry," Radiochim. Acta 88, 487-493 (2000).
[CrossRef]

Rev. Sci. Instrum.

M. G. Payne, L. Deng, and N. Thonnard, "Applications of resonance ionization mass spectrometry," Rev. Sci. Instrum. 65, 2433-2459 (1994).
[CrossRef]

Spectrochim. Acta Part B

B. A. Bushaw, W. Nortershauser, and K. Wendt, "Lineshapes and optical selectivity in high-resolution double-resonance ionization mass spectrometry," Spectrochim. Acta Part B 54, 321-332 (1999).
[CrossRef]

B. A. Bushaw and W. Nortershauser, Resonance ionization spectroscopy of stable strontium isotopes and 90Sr via 5s21S0 --> 5s5p 1P1 --> 5s5d 1D2 --> 5s11f 1F3 --> Sr," Spectrochim. Acta Part B 55, 1679-1692 (2000).
[CrossRef]

Other

B. A. Bushaw, W. Nortershauser, G. Ewald, A. Dax, and G. W. F. Drake, "Hyperfine splitting, isotope shift, and level energy of the 3S States of 6,7Li," Phys. Rev. Lett. 91, 043004 (2003).

G. Ewald, W. Nortershauser, A. Dax, S. Gotte, R. Kirchner, H.-J. Kluge, Th. Kuhl, R. Sanchez, A. Wojtaszek, B. A. Bushaw, G. W. F. Drake, Z.-C. Yan, and C. Zimmermann, "Nuclear charge radii of 8,9Li determined by laser spectroscopy," Phys. Rev. Lett. 93, 113002 (2004).

H. Haffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. Schmidt-Kaler, and R. Blatt, "Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor," Phys. Rev. Lett. 90, 43602 (4) (2003).

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, "Wavelength-dependent ac Stark shift of the 1S0-3P1 transition at 657 nm in Ca," Phys. Rev. A 70, 023414 (6) (2004).

M. Eisenbud, Environmental Radioactivity (Academic, 1987).

R. L. Kurucz and B. Bell, Atomic Line Data Kurucz CD-ROM No. 23 (Smithsonian Astrophysical Observatory, 1995).

R. L. Kurucz, 1988, Trans. IAU, XXB, M.McNally, ed., (Kluwer, 1966) 168-172.

W. L. Wiese, M. W. Smith, and B. M. Glennon, Atomic Transition Probabilities, Elements Hydrogen through Neon, NSRDS-NBS (Government Printing Office, 1966), p. 153.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, 1990).

B. A. Bushaw, "Diode-laser-based resonance ionization mass spectrometric measurement of calcium isotopes," Ph.D. dissertation (Johannes-Gutenberg Universitat, 1997).

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Figures (7)

Fig. 1
Fig. 1

Two-photon ionization schematic.

Fig. 2
Fig. 2

Variation of ionization efficiency and optical selectivity as a function of (A) the excitation laser power and (B) the ionization laser power for scheme 2. The power of the other laser is taken to be 1W. The filled symbols indicate selectivities while the open symbols indicate ionization efficiency: triangle, 100 μm; square, 75 μm; and circle, 50 μm.

Fig. 3
Fig. 3

Two-photon ionization line shape for schemes 1 and 2. The power of the excitation and ionization laser is 1 W, and the focusing diameter is 50 μm.

Fig. 4
Fig. 4

Ionization efficiency as a function of the detuning (A) before and (B) after Stark compensation has been plotted for scheme 6. The power of the excitation laser is 1W, and the power of the ionization laser is 5 W. The lasers have been focused to a diameter of 50 μ m .

Fig. 5
Fig. 5

Ionization yield as a function of power of the ionization laser for a 5 μ m focusing condition for scheme 2. The power of the excitation laser is taken to be 250 mW.

Fig. 6
Fig. 6

Time evolution of (A) excited level population and (B) ion yield for three different ionization laser powers. The excitation laser power is 250 mW, and the lasers have been focused to 5 μ m . P ion stands for the power of the ionization laser.

Fig. 7
Fig. 7

Time evolution of the excited level population and ion yield for three different ionization laser powers. (Time-independent Rabi frequency is considered for the evaluation of the density matrix equations.) P ion is the power of the ionization laser, and the excitation laser power is 250   mW .

Tables (2)

Tables Icon

Table 1 Two-Photon Rabi Frequency, ac Stark Shift of the Excitation and Ionization Lasers a

Tables Icon

Table 2 Ionization Efficiencies and Optical Selectivities for Different Focusing Conditions a

Equations (164)

Equations on this page are rendered with MathJax. Learn more.

8.4 × 10 - 4
9 × 10 3
10 16
5 s 2 ( S 1 0 ) 2 ϖ 5 p 2 ( S 0 1 )
2 s 3 s
2 s 3 s
(1) 4 s 2 ( S 0 1 ) 2 × 600.2896   nm 4 s 5 s ( S 0 1 ) 514.5   nm C a +
(2) 4 s 2 ( S 0 1 ) 2 × 491.5159   nm 4 p 2 ( S 0 1 ) 514.5   nm C a +
(3) 4 s 2 ( S 0 1 ) 2 × 478.6256   nm 4 s 6 s ( S 0 1 ) 514.5   nm C a +
(4) 4 s 2 ( S 0 1 ) 2 × 451.7054   nm 4 s 7 s ( S 0 1 ) 514.5   nm C a +
(5) 4 s 2 ( S 0 1 ) 2 × 435.8315   nm 4 s 8 s ( S 0 1 ) 514.5   nm C a +
(6) 4 s 2 ( S 0 1 ) 2 × 427.0305   nm 4 s 9 s ( S 0 1 ) 514.5   nm C a +
(7) 4 s 2 ( S 0 1 ) 2 × 418.0273   nm 4 s 11 s ( S 0 1 ) 514.5   nm C a +
S = P ( 0 ) P ( Δ ) ,
P ( 0 )
P ( Δ )
n s 2 S 0 1 2 ϖ n s m s ( or   n p 2 )
S 0 1 nonresonant M +
| 1
| 2
μ E ( t )
E i ( t ) = [ ε i ( t ) e i ω i t + ε i * ( t ) e i ω i t ] e i ,
e i
ε i ( t )
ρ ˙ 11 = i 2 ( Ω 12 * ρ 21 Ω 12 ρ 12 ) + 2 i γ i 1 ρ i i ,
ρ ˙ 22 = i 2 ( Ω 21 ρ 12 Ω 21 * ρ 12 ) 2 i γ 2 i ρ i i 2 γ I ρ 22 ,
ρ ˙ 12 = i Δ ( t ) ρ 12 + i Ω 12 * 2 ( ρ 22 ρ 11 ) ( i γ 2 i + γ I ) ρ 12 ,
ρ ˙ 21 = i Δ ( t ) ρ 21 i Ω 12 2 ( ρ 22 ρ 11 ) ( i γ 2 i + γ I ) ρ 21 ,
ρ ˙ i i = 2 i γ 2 i ρ 22 2 i γ i 1 ρ i i .
ρ j k
| j
j = k
j k
γ I = σ ϕ
| 2
γ 2 i
| 1
γ i 1
Ω 12
Δ ( t )
Δ ( t )
( Δ 0 )
[ ω 0 = ( E 2 E 1 ) / ħ ]
S ( t )
Δ ( t ) = Δ 0 + S ( t ) .
Δ ( t ) = E 2 E 1 2 ħ ω p + S 2 ( t ) S 1 ( t ) ,
ħ ω p
S j
| j
E 1
E 2
| 1
| 2
Ω 12 = i Ω 1 i ( 1 ) Ω i 2 ( 1 ) 2 Δ 1 i ,
Ω 1 i ( 1 )
Ω i 2 ( 1 )
| i
| 1
| 2
4 s 4 p P 1 o 1
A k i
A k i
W / c m 2
α ( ω )
I ( t )
S j = 1 2 ħ c ε 0 i j | α ( ω ) i | I ( t ) .
| j
| i
S j = i | μ j i | 2 4 ħ 2 Δ j i E 2 ,
Δ j i
| j
| μ j i | 2
| i
| j
| 2
| 1
S 12 = S 2 S 1 = i ( Ω 2 i 2 4 Δ 2 i Ω 1 i 2 4 Δ 1 i ) ,
Ω j i = μ j i E / ħ
| i
| j
P 1 o 1
4 s 4 p P 1 o 1
4 s 11 p P 1 o 1
3 d 4 p P 1 o 1
4 s 2 S 0 1
4 s n s S 0 1
( 1 ) Ω ( t ) = Ω 0 I ( t ) ,
( 2 ) S ( t ) = S 0 I ( t ) ,
( 3 ) γ I ( t ) = γ 1 0 ( t ) ,
Ω 0
S 0
γ 0
1000 °   K
10 - 17 cm 2
n s 2 S 0 1 2 ϖ n s m s S 0 1 nonresonant M +
I 0 / 2
| m = 0 | m = 0
| m = 0 | m = ± 2
50   mW
1   mm
6.3 W / cm 2
50   mW
1   W
100 μ m
50 μ m
50 μ m
1   W
1   W
25 μ m
2.5 × 10 4
2.1 × 10 - 3
5   W
75 μ m
1.6 × 10 4
50 μ m
( 10 - 5 )
( 112   MHz )
3 ( 4 s 6 s S 0 1 )
30   MHz
4 s 6 s S 0 1
( 0.6   MHz )
( 4 s 8 s S 0 1 )
( 112   MHz )
30   MHz
( 850   MHz )
S E I E + S I I I = 0 ,
S E
I E
W / cm 2
S I
I I
W / cm 2
25 μ m
5 μ m
350   mW
5 μ m
150   mW
850   mW
850   mW
350   mW
850   mW
Ω ˜ = | Ω | 2 + ( ω 0 ω ) 2 + ( γ 2 γ 1 ) 2 ,
( ω 0 ω )
γ 1
γ 2
150   mW
250   mW
| Ω | 2
( ω 0 ω ) 2
( γ 1 γ 2 ) 2
1.97 × 10 15 Hz 2
3.6 × 10 15 Hz 2
4.31 × 10 16 Hz 2
( ρ 22 )
50 μ m
8 .4 × 10 - 4
9 × 10 3
W / c m 2
50 μ m
5 μ m
5 μ m
P ion
P ion
250   mW

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